264 Part 3: Stocks and Options
b. (1) Why is the T-bill's return independent of the state of the economy? Do T-bills promise a completely risk-free return? (2) Why are Alta Industries's returns expected to move with the economy whereas Repo Men's are expected to move counter to the economy? c. Calculate the expected rate of return on each alternative and fill in the blanks in the row for in in the table. d. You should recognize that basing a decision solely on expected returns is appropriate only for risk-neutral individuals. Because your client, like virtually everyone, is risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of returns. (1) Calculate this value for each alternative, and fill in the blank in the row for o in the table. (2) What type of risk is measured by the standard deviation? (3) Draw a graph that shows roughly the shape of the probability distributions for Alta Industries, American Foam, and T-bills. e. Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as being a better measure of stand-alone risk than the standard deviation when the alternatives being considered have widely differing expected returns. Calculate the missing CVs, and fill in the blanks in the row for CV in the table. Does the CV pro-duce the same risk rankings as the standard deviation? f. Suppose you created a two-stock portfolio by investing $50,000 in Alta Industries and $50,000 in Repo Men. (1) Calculate the expected return (0, the standard deviation (or,), and the coefficient of variation (CVO for this portfolio and fill in the appropri-ate blanks in the table. (2) How does the risk of this two-stock portfolio compare with the risk of the individual stocks if they were held in isolation? g. Suppose an investor starts with a portfolio consisting of one randomly selected stock. As more and more randomly selected stocks are added to the portfolio, what happens to the portfolio's risk and its expected return? What is the implication for investors? Draw a graph of the two portfolios to illustrate your answer. h. (1) Should portfolio effects influence how investors think about the risk of individual stocks? (2) If you decided to hold a one-stock portfolio and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all of your risk; that is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying? i. How is market risk measured for individual securities? How are beta coefficients calculated? j. Suppose you have the following historical returns for the stock market and for the company P. Q. Unlimited. Explain how to calculate beta, and use the historical stock returns to calculate the beta for PQU. Interpret your results.
Year
Market PQU
1 25.7% 40.0% 2 8.0 -15.0 3 -11.0 -15.0 4 15.0 35.0 5 32.5 10.0 6 13.7 30.0 7 40.0 42.0 8 10.0 -10.0 9 -10.8 -25.0 10 -13.1 25.0
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Chapter 6: Risk, Return, and the Capital Asset Pricing Model 265
k. The expected rates of return and the beta coefficients of the alternatives, as supplied by Barney Smith's computer program, are as follows:
Security Return CI') Risk (Beta)
Alta Industries 17.4% 1.29 Market 15.0 1.00 American Foam 13.8 0.68 T-bills 8.0 0.00 Repo Men 1.7 —0.86
(1) Do the expected returns appear to be related to each alternative's market risk? (2) Is it possible to choose among the alternatives on the basis of the information developed thus far? 1. (1) Write out the Security Market Line (SML) equation, use it to calculate the required rate of return on each alternative, and then graph the relationship between the expected and required rates of return. (2) How do the expected rates of return compare with the required rates of return? (3) Does it make sense that Repo Men has an expected return that is less than the T-bill rate? (4) What would be the market risk and the required re-turn of a 50-50 portfolio of Alta Industries and Repo Men? Of Alta Industries and American Foam? m. (1) Suppose investors raised their inflation expectations by 3 percentage points over current estimates as reflected in the 8% T-bill rate. What effect would higher inflation have on the SML and on the returns required on high- and low-risk securities? (2) Sup-pose instead that investors' risk aversion increased enough to cause the market risk pre-mium to increase by 3 percentage points. (Assume inflation remains constant.) What effect would this have on the SML and on returns of high- and low-risk securities?
CTED ADDITIONAL CASES The following cases from Textchoice, Cengage Learning's online library, cover many of the concepts discussed in this chapter and are available at http://www. textchoice2. corn. Klein-Brigham Series: Case 2, "Peachtree Securities, Inc. (A)." Brigham-Buzzard Series: Case 2, "Powerline Network Corporation (Risk and Return)."